Any ideas why MyDAQ's Bode looks like this ?
You don't have a whole lot of signal there at the higher attenuations so I think those are just artifacts of the measurement.
If the behavior deep into the stop band of your MFB filter is really of keen interest, try to increase the signal levels to as high as your ADC can handle without clipping. You have only 16 bits so the the quantization noise will limit you around -95dB. There is probably significantly more noise than that in the ADC. If that doesn't work well enough for your requirements, get a better ADC or even try a sound card.
You are misinterpreting your graphs. A wildly-swinging phase response is not oscillation. I suggest you try providing a nominal zero volts DC in, and do a transient response analysis of the output, and I suspect you'll see no oscillation. If there is any, it will be at microvolt levels, and will be an artifact of the simulator.